1. Field of the Invention
This invention relates in general to constraint based curve design, and more particularly, to a method, apparatus, and article of manufacture for generating regularized tangents of curves.
2. Description of Related Art
Lines, curves, arcs, and splines are used in 3D Computer Aided Design (CAD) systems and vector graphics systems to indicate surfaces, edges, and other geometric shapes.
Typically, magnitudes of tangents to splines, arcs, and curves are estimated by the user. This magnitude estimation at endpoints and/or midpoints on the curves lead to errors in computations based on the improperly estimated tangents, leading to wasted materials, time, and effort. The direction of a tangent is a geometric idea that a user is comfortable with in solving equations involving derivatives, which require direction and magnitude, but the magnitude has no geometric reference for the user.
Therefore, there is a need in the art for a way to generate tangents that is more intuitive. There is also a need in the art for a way to quickly generate tangents for an arc or curve. There is also a need in the art to be able to quickly generate tangents at endpoints of an arc or curve.
To overcome the limitations in the prior art described above, and to overcome other limitations that will become apparent upon reading and understanding the present specification, the present invention discloses a method, apparatus and article of manufacture for generating regularized tangents of curves. The method comprises the steps of bounding a length of the arc, computing a chord vector, where the chord vector corresponds to the bounded length of the arc, generating a tangent vector, where the tangent vector is substantially normal to the chord vector, and regularizing the tangent vector, where the regularized tangent vector approximates a true tangent vector to the arc.
An object of the present invention is to provide a method for generating tangents that is more precise. Another object of the present invention is to provide a method for quickly generating tangents for an arc or curve. Still another object of the present invention is to provide a method for quickly converting tangents to derivatives at endpoints of an arc or curve.